Attenuation and wavelet distortion have been observed on seismic data due to anelastic properties of the earth. For example, strong attenuation of seismic P-waves can result from gas trapped in overburden structures. As a result, not only is the migrated amplitude below the gas anomaly dim, but also the imaging resolution is greatly reduced by the high frequency energy loss and the phase distortion. In seismic processing, mitigating these undesirable effects can improve a final image and make it easier to interpret.
In complex media, Q-effect compensation techniques that do not take into account the wavepath or raypath information usually fail at mitigating Q-effects properly. As one-way wave equation migrations are formulated in the frequency domain, one can address frequency dependent dissipation. Reverse-time migration (“RTM”) that is based on directly solving the two-way wave equation has provided a superior way to image complex geologic regions, and has recently become a standard migration tool for subsalt imaging. One can also incorporate Q-effect correction capabilities into a frequency domain implementation of RTM. To incorporate Q-effect correction capabilities into a conventional implementation of RTM, however, there is a need to formulate a time domain wave equation to model the Q-effect effects. Moreover, the backward propagation of the receiver wavefield in RTM that includes Q-effect correction can be improved by model amplification. Furthermore, in some instances, it can be desirable to approximate integration over a wavepath to improve imaging conditions, which can have applications going beyond Q-effect correction.
Accordingly, there is a need for methods and systems that can employ, more efficient, and more accurate methods for processing and imaging of collected data, such as filtering wavefields to compensate for amplitude and/or phase effects before imaging. Such methods and systems may complement or replace conventional methods and systems for processing and imaging collected data.